lim【1/x-1/(e^x-1)】,x→0.

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lim【1/x-1/(e^x-1)】,x→0.
lim【1/x-1/(e^x-1)】,x→0.

lim【1/x-1/(e^x-1)】,x→0.
lim【1/x-1/(e^x-1)】
=lim (e^x-1-x)/x(e^x-1)
=lim (e^x-1)/[(e^x-1)+xe^x]
=lim 1/[1+xe^x/(e^x-1)]
=lim 1/{1+e^x/[(e^x-1)/x]}
=1/(1+1/1)
=1/2

lim【1/x-1/(e^x-1)】
=lim (e^x-1-x)/x(e^x-1)
=lim (e^x-1)/[(e^x-1)+xe^x]
=lime^x/(2e^x+xe^x)
=1/（2+0）=1/2

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